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boneill3
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Homework Statement
Find an Basis for Image and Kernel of the matrix.
[itex]\[ \left( \begin{array}{ccc}
2 & 1 & 3 \\
0 & 2 & 5 \\
1 & 1 & 1 \end{array} \right)\]
[/itex]
Homework Equations
The Attempt at a Solution
To find the kernel I solve the equation Ax = 0
I put the matrix in row reduced echelon form which is the identity matrix.
[itex]
\[ \left( \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \end{array} \right)\]
[/itex]
Therefore its the equation
x = 0
y = 0
z = 0
The kernel basis is just the unit basis, {(1,0,0),(0,1,0),(0,0,1)}
For the image basis I've seen that you can use the pivots of the rref matrix and use the corresponding column vectors of the original Matrix as the image basis.
So is that just
{(2,0,1),(1,2,1),(3,5,1)} ?
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